A unified model for fracture mechanics

Abstract

Since Irwin's [1, 2] pioneering contribution to the field of fracture mechanics, in which his concept of stress intensity factor ( K I or K II) was first introduced, there has been some apparent inconsistency of developments in the discipline. The anomaly, which may be mainly attributed to an oversight of the restriction by Irwin's derivation of fracture toughness ( K IC or K IIC) to a crack propagating in its own plane (where θ C = θ 0C = 0), has probably been aggravated by the difficulty inherent in generating a true shear fracture physically. A common case in point has been the attribution of a tensile fracture propagating at θ C = −70·5° from an existing crack tip, which is subjected to pure mode II loading along the θ = θ 0 = 0 plane, to a shear “fracture” instead. It would appear that the reason for doing so has been the commonly-held assumption that a pure mode of loading on the θ 0 plane would result unconditionally in the same mode of fracture. The apparent basis for the assumption has, in turn, been the widely-accepted—although unjustified—concept that the stress intensity factor is an absolute constant of a given boundary value problem, whereas it should, by right, be considered as dependent on the angle of interest θ to an existing crack plane. In these circumstances, a unified model has been developed as a natural extension as well as generalisation of Irwin's approach. In contrast with the approach, which caters only to pure mode fracture along the θ 0C direction due to pure mode loading on the θ 0 plane, consideration may be given to either pure or mixed mode crack propagation along the general θ C plane (where − π < θ C < π), due to either pure or mixed mode applied loading. In order to achieve this, it has been found necessary to make a distinction between traditional stress intensity factors K I and K II, which are noteworthy only in that they may be related directly to corresponding pure modes of applied loading in the far field (as referred to the θ 0 plane), and proposed unified stress intensity factors K I θ and K II θ , respectively, which would be actually instrumental in determining the development of fracture in the generalised θ C direction. The unified model may be represented by a fracture surface defined in terms of fracture toughness ratio K CR and normalised, traditional modes I and II stress intensity factors, K IR and K IIR, respectively. A notional example is presented herein, with the qualification that, for a given material, the determination of its precise surface would, in principle, require a rigorous programme of experimental verification based on a generalised fracture envelope such as proposed. By means of the unified model, various inconsistencies that have arisen in fracture mechanics since Irwin's pioneering work may be rationalised and hence resolved. In addition, the proposed model may be substantiated by currently available experimental evidence; in particular, the model can predict the systematic propagation of true shear fracture with reasonable accuracy, which has apparently not been the case hitherto.